Abstract
We introduce a class of topologically transitive and partially hyperbolic sets called porcupine-like horseshoes. The dynamics of these sets is a step skew product over a horseshoe. The fiber dynamics is given by a one-dimensional genuinely noncontracting iterated function system. We study this dynamics and explain how the properties of the iterated function system can be translated to topological and ergodic properties of the porcupines.
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Acknowledgements
This paper was partially supported by CNPq (research grants and Projeto Universal), CNE Faperj, and Pronex (Brazil) and Balzan Research Project of J. Palis.
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Díaz, L.J., Gelfert, K. (2013). Porcupine-Like Horseshoes: Topological and Ergodic Aspects. In: Ibáñez, S., Pérez del Río, J., Pumariño, A., Rodríguez, J. (eds) Progress and Challenges in Dynamical Systems. Springer Proceedings in Mathematics & Statistics, vol 54. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38830-9_12
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